Question

A ball of mass $2\text{kg}$ and another of mass $4\text{kg}$ are dropped together from a $60$ feet tall building. After a fall of $30$ feet each towards earth, their respective kinetic energies will be in the ratio of -

• A. $1:4$
• B. $1:2$
• C. $1:\sqrt{2}$
• D. $\sqrt{2}:1$

Answer 1

The correct option is B $1:2$

Given :

$m_1=2\text{kg}$
$m_2=4\text{kg}$

Since, both the balls fall through the same distance under the gravitational force, their velocities will be same as $v=\sqrt{2gh}$.

Now,

$\frac{K{E}_1}{K{E}_2}=\frac{\frac{1}{2}{m}_1{v}^2}{\frac{1}{2}{m}_2{v}^2}$

$\Rightarrow \frac{K{E}_1}{K{E}_2}=\frac{m_1}{m_2}=\frac{2}{4}=\frac{1}{2}=1:2$

​​​​​​​Hence, option $\left(B\right)$ is the correct answer.